# Anisotropic cosmological models in $f(R,T)$ gravity with variable deceleration parameter

## TL;DR

This paper investigates anisotropic Bianchi type-I cosmological models within $f(R,T)$ gravity, considering variable deceleration parameters and bulk viscosity, to understand universe acceleration and compatibility with observational data.

## Contribution

It provides exact solutions for anisotropic $f(R,T)$ gravity models with bulk viscosity and analyzes their physical properties and observational consistency.

## Key findings

- Both models exhibit accelerated cosmic expansion.
- Models satisfy energy conditions and are compatible with observational data.
- Cosmic jerk parameter aligns with kinematical datasets.

## Abstract

The objective of this work enclosed with the study of spatially homogeneous anisotropic Bianchi type-I universe in $f(R,T)$ gravity (where $R$ is the Ricci scalar and $T$ is the trace of stress energy momentum tensor) in two different cases viz. $f(R,T)=R+2f(T)$ and $f(R,T)=f_1(R)+f_2(T)$ with bulk viscosity matter content. In this study, we consider a time varying deceleration parameter, which generates an accelerating universe to obtain the exact solution of the field equations. The physical and kinematical properties of both the models are discussed in detail for the future evolution of the universe. We have explored the nature of WEC, DEC, SEC and energy density for both the cases. We have found that both the models, with bulk viscosity matter component, show an acceleration of the universe. We have also shown that the cosmic jerk parameter is compatible with the three kinematical data sets.